That flawed diamond could be a quantum physicist’s best friend

Elisabeth Rülke is working to improve quantum sensing for her senior thesis research at Princeton University

Shoppers like flawless diamonds, but for quantum physicists, the flaws are the best part.

Senior Elisabeth Rülke has spent the past year using lasers and flawed diamonds — tiny wafers of diamond with flaws the size of a single atom — to develop a quantum sensor.

The clear wafer at the center of the equipment is a diamond plate, precisely manufactured to be 2 mm on a side and .3 mm thick, with atomic-sized flaws at which Rülke and her adviser Nathalie de Leon shine green and orange lasers.

Unlike quantum computers, which are still more theoretical than practical, quantum sensors are already in use. Rülke and her adviser, quantum physicist Nathalie de Leon, are working on a new approach to quantum sensing that depends on using two of these single-atom defects simultaneously.

"Because they are so, so small, you could begin to map and sense things on a scale that has never been feasible before," said Rülke, a physics concentrator pursuing a certificate in applied and computational mathematics. "It would be revolutionary to chemistry, biology and especially medical devices."

"Working with very bright students like Elisabeth is always just a privilege," said de Leon, an associate professor of electrical and computer engineering who is associated faculty in the physics department. "She brings a fresh perspective and a different take on things, and that brought a little more creativity on the project than I think would have happened otherwise. I’m lucky to be at Princeton and get these really great students knocking on my door."

Rülke knew before she came to Princeton that she wanted to study physics and astronomy, but she also knew that she wanted to take full advantage of the liberal arts. "I have taken courses in history, philosophy, religion, entrepreneurship, film, art and others, and I believe it has been a cornerstone of my Princeton experience. The wonderful part about Princeton's liberal arts education is that it allows you to take classes in a range of subjects, meaning that what you choose to major in isn't the only focus of your education, as is the case with most British universities and a strong reason why I wanted to study in the U.S.," said Rülke, who was born and raised in London.

"I do think that there is overlap in the critical and creative thinking used in both higher-level physics and mathematics courses and the humanities subjects," she added.

When Princeton closed its campus to in-person instruction in March of Rülke's first year, she went home to London for Zoom classes. That summer, when travel restrictions eased, she and a Princeton classmate moved into an apartment in Rome. "I took an art history class that fall, and it was amazing," Rülke said. "I remember one assignment asked us to go find art ‘wherever you are.’ Most of my classmates looked at, like, a teapot from their house, and I chose a Bernini sculpture."

After she returned to campus, she decided to focus her first junior paper on a truly enormous question: the nature of dark energy in the universe.

"She hadn't had a course in general relativity, she hadn't had a course in cosmology, and she wasn't daunted at all," said Paul Steinhardt, Princeton's Albert Einstein Professor in Science and a professor of physics who was her adviser on that paper. "It was clearly a stretch for her, but she was just full of energy and enthusiasm. I really enjoy seeing a student stretching and learning, and that certainly characterized Elisabeth. She broke her leg that semester, but she still always came to our weekly meetings with enthusiasm and cheer and lots of great research questions."

After they worked together on that paper, Steinhardt served as the second reader on Rülke's second junior paper, then reprised that role for her senior thesis. "I’ll have read all her theses by the time we’re through," he said.

Rülke came to Princeton knowing she wanted to immerse herself in STEM — science, technology, engineering and mathematics — and specifically in physics and astronomy.

"The Princeton astrophysics and physics departments are absolutely amazing," she said. "I feel so lucky. When I visited Princeton after I got in, I went to go see Einstein's old classroom and walked to his house, which is near campus."

In the lab, Rülke performs a confocal scan to locate NV centers in a diamond lattice.

After tackling theoretical cosmology for her first independent research project, she wanted to try something more hands-on, so she did her second junior paper on plasma propulsion. "Both were very, very interesting. The first one was very theoretical, and the second was almost too experimental," she said. "I was actually climbing into a thrust tank with tools and tinkering with stuff in there. So for my thesis, I wanted something in the middle."

Her broad perspective has served Rülke well as she tackles quantum sensing, a problem that has brought together professors from physics, chemistry and engineering with the goal of tackling a large range of problems, from biophysics and biomedical applications to condensed matter physics and designing new navigational sensors.

"The general ethos of my research group is to try to see problems without any borders as much as possible," said de Leon. "Our approach to problems tends to start with, ‘What does it take to solve this? We have all of physics and all of chemistry and all of materials engineering — all the tools of humanity — so let's see if we can MacGyver our way to a solution.’ Elisabeth definitely fit in like a fish in water."

Diamonds are made of pure carbon, as are charcoal and the graphite in pencils. But you can write with pencils (and charcoal) because those carbon atoms are organized in sheets that slide apart with the barest pressure, leaving marks behind.

The carbon atoms in a diamond, by contrast, have been forced together with tremendous pressure, crowding the atoms together in a perfect and complex web. This allows for another unique property: when a nitrogen atom pushes in and displaces two carbon atoms, it creates a tiny defect called a "nitrogen vacancy center" or "NV center."

NV centers behave like tiny compass needles and have been used in quantum sensors that can measure magnetic fields. While quarantining at home during the COVID pandemic, de Leon began wondering what would happen if there were two NV centers, precisely separated within a diamond chip.

It turns out that while it's much, much harder to measure two nitrogen vacancies simultaneously, once you do, you can measure new physical quantities, namely correlations in the magnetic field in space and time. With simultaneous measurements of two NV centers, a whole new world of nanoscale measurements is possible, de Leon said.

"This is a fundamentally new thing," she said. "The world is our oyster. We can use this new technique that measures a completely new physical quantity. So let's clean up! Let's go look at everything that people were trying to do in the ‘80s and then just got stuck because they didn't have the right tool. Maybe there's some really cool physics that we can learn. That's where Elisabeth comes in."

The voyage from pandemic inspiration to simultaneously measuring two NV centers took years. De Leon and a postdoc in her lab, Jared Rovny, spent 18 months working out the math and longer than that to figure out how to build a tool that lets you shine lasers at two atomic-sized objects and then count the photons flying out. They first demonstrated this technique with a resolution of 500 nanometers. (For comparison's sake, the period at the end of this sentence is about a million nanometers across.) Rülke's senior thesis has focused on improving this resolution from 500 nanometers down to 10 nm or maybe even a single nanometer.

Rülke credits her coursework and her independent research projects at the University with developing her ability to navigate uncertainty and face challenges head-on.

"I remember a three-hour physics exam that only had two questions. You have to spend so much time grasping around in the darkness, trying to think of how to do this, which method to start with — and building the skills to do that makes you a person with the ability to think really critically and not be afraid if you’re going head-on to a problem where you can't really see the end or you don't really know how to solve it.

"In high school, I hated those sorts of problems," she said. "I liked getting to the answer and getting it right. That growth happened at Princeton."

She and de Leon both enjoyed their weekly thesis advising sessions.

"I have enough autonomy to decide what exactly I want to do," Rülke said. But de Leon also provides enough help "to make sure that I have the right background knowledge."

"She always shows up at my office extremely sunny and very enthusiastic," de Leon said of Rülke. "I don't know where she gets all that energy. Even if it's the middle of midterm season or application season, she still just shows up and is like, ‘Okay, here's what I’ve done. Look at all my data. Let's discuss it. Here's my plan. I think this thing is really interesting.’"

Rülke and her thesis adviser, quantum physicist Nathalie de Leon (right), are measuring two nitrogen vacancy centers simultaneously. De Leon and her postdoc Jared Rovny first demonstrated this technique with a resolution of 500 nanometers, and Rülke's senior thesis has focused on improving this resolution down to 10 nm or maybe even a single nanometer.

Rülke gives her parents a tour of Cottage Club in Fall 2022.

Outside of her coursework, Rülke is a member of Mathey College and she serves as the diversity, equity and inclusion chair of University Cottage Club. She got involved in entrepreneurship through the Keller Center and the Entrepreneurship Club, and she traveled to California with the Silicon Valley Tiger Track to meet with entrepreneurs, venture capital firms and space related companies.

She received the Manfred Pyka Memorial Prize in Physics, given to outstanding physics undergraduates who have shown excellence in course work and promise in independent research; the Jocelyn Bell Burnell fellowship, aimed at encouraging women to pursue physics; and the Schwarzman Scholarship, which covers the cost of one-year master's program at Tsinghua University in Beijing.

Rülke says she feels "a pull towards being a global citizen," having been born in the United Kingdom to a German dad and a Chinese mom.

"My cultural identity is complicated," she said. "I have family in different parts of the world, and sometimes being mixed race means you don't feel that you fully fit in anywhere. Visiting family in Germany or in China, I never looked like anybody else.

"As a kid, that made me feel out of place sometimes, but as I’ve grown up, I’ve started to enjoy it," Rülke said. "I think standing out is much better than disappearing into a crowd."

This elaborate array of mirrors, lenses, and scanning galvonometers route and collect light in this home-built microscope for quantum sensing.

Rülke dons safety safety goggles before firing lasers into single-atom sized defects that are closer together than the wavelength of light.

Rülke (left) visits Cairo with her family in 2009.

Elisabeth Rülke is a Class of 2023 physics major with a minor in applied and computational mathematics.